If \((\vec{a} \times \vec{b}) \times \vec{c}= \vec{a} \times (\vec{b} \times \vec{c})\), then
Expand the triple product: \[ (a \cdot c) b - (b \cdot c) a = (a \cdot c) b - (a \cdot b) c. \] This simplifies to: \[ (b \cdot c) a = (a \cdot b) c. \] Since \( b \cdot c \) and \( a \cdot b \) are scalar quantities, we conclude that \( a \) and \( c \) are collinear vectors.
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